The former England centre-back was due in the north-east this afternoon for a medical before securing another season in the Premier League.
Campbell had also been linked with Newcastle's local rivals Sunderland and Celtic following the end of his short-term contract at Arsenal but the 35-year-old appears to have decided on a move to St James' Park.
The deal would see Campbell reunited with Magpies boss Chris Hughton, with whom he worked at Tottenham early in his career.
Hughton, who was also linked with Campbell before he decided on a return to Arsenal last season, has been eager to strengthen his defence in the face of injury problems.
The club are still waiting to discover the full extent of Steven Taylor's shoulder injury while new signing James Perch is sidelined with a heel problem.
Taylor is set to at least miss the start of the campaign, which Newcastle begin away to Manchester United on August 16, but there are fears he could be sidelined for several months, prompting Hughton to make his move for Campbell.
Sunderland's interest in the former England international had diminished in recent weeks after they signed former Magpies defender Titus Bramble from Wigan, while they are also expected to loan John Mensah for another season from Lyon.
Campbell was married in Northumberland earlier this month and has only recently returned from his honeymoon, after which he had indicated a decision on his future would be made public.
The central defender made a shock return to the Premier League for a second spell with Arsenal last season, after he had signed for then League Two side Notts County.
Campbell left the Magpies after just one match before rejoining the Gunners on a short-term deal that expired earlier this summer.
The 35-year-old, who won the last of his 73 England caps in 2007, began his career with Tottenham before ending an 11-year stay at White Hart Lane with a controversial move to their arch-rivals Arsenal in 2001.
Five years later he moved on again, to Portsmouth, where he won the FA Cup for the fourth time.
The defender would be Newcastle's third summer signing after the arrivals of Perch and Everton youngster Dan Gosling.
Meanwhile, former Magpies and England forward Peter Beardsley has moved from his coaching role within the club's academy to become reserve-team coach.
The 49-year-old, who will be assisted by former England winger Steve Stone, succeeds Alan Thompson after his move to Celtic at the end of last season.
Beardsley told www.nufc.co.uk: "This is a fantastic opportunity for me and one that I am thrilled to have been given. I can't wait to get cracking with what I know are a very talented set of players."